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njwildberger.com | ||
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jdh.hamkins.org
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| | | | | This will be a series of lectures on the philosophy of mathematics, given at Oxford University, Michaelmas term 2018. The lectures are mainly intended for undergraduate students preparing for exam ... | |
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notageni.us
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| | | | | Most people in modern society have been trained in arithmetic and algebra from childhood, but don't often know what math is. The Basis of Math Every concept in math is a precisely parsed concept in an imaginary space. While some numbers represent real things (e.g., 2, 3) and are therefore called "real numbers", others can [...]Read More... from Defining Math | |
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carcinisation.com
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| | | | | Gödel's theorems say something important about the limits of mathematical proof. Proofs in mathematics are (among other things) arguments. A typical mathematical argument may not be "inside" the universe it's saying something about. The Pythagorean theorem is a statement about the geometry of triangles, but it's hard to make a proof of it using nothing... | |
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xorshammer.com
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| | | We think of a proof as being non-constructive if it proves "There exists an $latex x$ such that $latex P(x)$ without ever actually exhibiting such an $latex x$. If you want to form a system of mathematics where all proofs are constructive, one thing you can do is remove the principle of proof by contradiction:... | ||
